Explain how the special formulas for the mean and standard deviation of a binomial or Poisson random variable are derived.

Q: 1.) enumerate the steps for a hypothesis test for a population mean when the variance is known.

A: STEPS FOR HYPOHESIS TEST FOR A POPULATION MEAN 1) State the hypothesis i.e. Null and Alternative…

Q: What is the main difference between Binomial distribution and the Poisson's distribution?

A: Given, Binomial and Poisson distribution To explain the difference between the Binomial and Poisson…

Q: Explain the significance of the mean, variance, and standard deviation for a random variable. Do the…

A: Significance of mean, standard deviation and variance is – Mean: it implies average and the sum of…

Q: Last​ year, a person wrote 128 checks. Let the random variable x represent the number of checks he…

A: Let λ is the mean number of checks written per day, then λ=128365, assuming there are 365 days in…

Q: Suppose I have an unfair coin, it lands on heads 75% of the time.  If I flip this coin four times,…

A: Binomial distribution: The binomial distribution gives the probability of number of successes out of…

Q: How do you illustrate a normal random variable?

A: How do you illustrate a normal random variable?

Q: Determine the Binomial distribution for which the mean is 4 and variance 3 and find its mode.

A:

Q: Suppose you throw two dice and take the sum as a discrete random variable. Let us assume you take a…

A: When you throw two dices together, each dice will show a number ranging from 1 to 6 on the side…

Q: What is the moment generating function of the sample mean?

A: Mgf (i)Sample mean=x⏞=Σxin=x1+x2+..+xn10…

Q: What is it meant by the term “parameter of a population”? Explain why a population can be…

A:

Q: What is the expected value of a continuous random variable? What is the expected value of an…

A: Definition used:

Q: A random variable that can be used of the gamma distribution is

A: Random variable can be α=4,β Mean and variance can be, E(X)=αβ=4βVar(X)=αβ2=4β2 Size of sample is…

Q: How can we calculate the probability-weighted average of the squared deviations?

A:

Q: Can a normal distribution always be used to approximate a binomial distribution?

A: we can use normal distribution to approximate a binomial t

Q: Using matlab, calculate a random variable with mean=-3 and standard deviation=1

A: Given data, mean=-3 and standard deviation=1

Q: What is the median of a continuous random variable? What is the median of an exponential…

A:

Q: What value is the probability that the mean of nine randomly selected individuals from a normally…

A: Sampling distribution of the sample mean x¯ ~ N(μx¯ , σx¯)

Q: The number of computers sold per day   at a local computer store are 0 , 1 , 2 , 3 , 4 and its…

A: Given: Probability distribution for number of computers sold per day at a local computer store. The…

Q: A hypergeometric and a Poisson probability distribution have the same mean. Which has the larger…

A: If one were to see that r/N (of the hypergeometric Distribution) is similar to p, The expected…

Q: Make a critical summary of the binomial probability distribution and the normal distribution.

A: summary of the binomial probability distribution and the normal distribution.

Q: What is the binomial distribution?

A: The binomial probability distribution is a discrete probability distribution in which the outcomes…

Q: Discuss how to estimate probabilities empirically using simulations.

A: Initially using simulation we obtain sample of any large size( 100,500,1000,5000 etc.) from the…

Q: One of the characteristics of a standard normal curve is that its variance and standard deviation is…

A: We want to tell you which one is the correct choice

Q: If other factors are held constant, as the sample variance increases, the estimated standard error…

A: Given: Sample variance increase and effect on the estimated standard error

Q: What is the difference between uniform distribution and binomial distribution?

A: The two distributions which are given are Uniform distribution and Binomial distribution.

Q: A normally distributed random variable has a mean of 140 and a variance of 2575. What is the…

A: μ = 140σ2=2575→σ = 2575 = 50.74

Q: Explain Multivariate Gaussian probability distribution.

A: Multivariate Gaussian Probability distribution is also known as Multivariate normal probability…

Q: TRUE OR FALSE. If the population variances are unknown but can be assumed to be equal, a pooled…

A: Given the statement  that if the population variances are unknown  but can be assumed to be equal, a…

Q: How to find the expected value and variance of a beta from a Gamma distribution?

A: Pdf of gamma distribution is

Q: Jimmy has an unfair coin that he flips and it lands on heads 75% of the time. If he flips this coin…

A: Jimmy's unfair coin lands on head 75% of the time. Hence probability that, the coin will lands on…

Q: What is the variance of random variables X, the outcome of rolling a fair die

A: The sample of rolling a fair die is {1,2,3,4,5,6}.

Q: Consider a Bernoulli Experiment with 7 trials. If the expected number of “successful” trials is 4,…

A:

Q: How do you describe a discrete random variable?

A: A RANDOM VARIABLE IS A NUMBER GENERATED BY RANDOM EXPERIMENT RANDOM VARIABLES ARE OF TWO TYPES:…

Q: Derive the mean and the variance of Poisson Distribution

A: The p.m.f. of Poisson distribution is given by P(X=x)=e-m  mxx!        ; x=0,1,2,....…

Q: What is the difference between a Binomial distribution and a Poisson distribution?

A:

Q: when can a normal distribution be used to approximate a binomial distribution?

A: Introduction to binomial distribution:Consider a random experiment involving n independent trials,…

Q: how can you use the concepts of the mean variance and standard deviation of the probability…

A: Mean: Mean for a probability distribution is the average expected return from the gamble It means…

Q: What concept does the mean of a discrete random variable generalize?

A:

Q: Formulate the standard deviation of the binomial distribution ?

A: Formula for  standard deviation of the binomial distribution  is Sqrt[npq] where n= number of trials…

Q: What is the mean and variance of a variable that follows the binomial distribution?

A: Let X be the random variable follows binomial distribution.  X ~ Binomial (n, p)

Q: Describe the procedures on how to use the normal probability distribution?

A: The normal probability distribution is basically used when there is a need to find the probability…

Q: a) Briefly explain in your own words with clear examples what you understand by binomial and Poisson…

A: We will give definition and example binomial and poisson distribution with examples

Q: Last​ year, a person wrote 116 checks. Let the random variable x represent the number of checks he…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.